The present ratio of age of A & B is 3 : 5. If the sum of present age of A & B is 48 years. Find the ages of A & B before 5 years.

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Given Information
We know that the present ratio of ages of A and B is 3:5, and the sum of their present ages is 48 years.

### Step 2: Set Up the Ratio
Let the present age of A be \(3x\) and the present age of B be \(5x\), where \(x\) is a common multiplier.

### Step 3: Write the Equation for the Sum of Ages
According to the problem, the sum of their ages is:
\[ 3x + 5x = 48 \]

### Step 4: Simplify the Equation
Combine like terms:
\[ 8x = 48 \]

### Step 5: Solve for \(x\)
Now, divide both sides by 8 to find \(x\):
\[ x = \frac{48}{8} = 6 \]

### Step 6: Find the Present Ages of A and B
Now substitute \(x\) back into the expressions for A and B:
- Present age of A:
\[ A = 3x = 3 \times 6 = 18 \text{ years} \]
- Present age of B:
\[ B = 5x = 5 \times 6 = 30 \text{ years} \]

### Step 7: Calculate Ages Before 5 Years
Now, we need to find their ages 5 years ago:
- Age of A 5 years ago:
\[ A_{5 \text{ years ago}} = 18 - 5 = 13 \text{ years} \]
- Age of B 5 years ago:
\[ B_{5 \text{ years ago}} = 30 - 5 = 25 \text{ years} \]

### Final Answer
Thus, the ages of A and B before 5 years were:
- Age of A: 13 years
- Age of B: 25 years

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